{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NGZCXJ2H4M6Z64LLW7RZCF5PHI","short_pith_number":"pith:NGZCXJ2H","schema_version":"1.0","canonical_sha256":"69b22ba747e33d9f716bb7e39117af3a023ec77791f4d967f9132e61b49cd0a9","source":{"kind":"arxiv","id":"1606.00071","version":1},"attestation_state":"computed","paper":{"title":"A fully nonlinear Sobolev trace inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeffrey S. Case, Yi Wang","submitted_at":"2016-05-31T23:09:25Z","abstract_excerpt":"The $k$-Hessian operator $\\sigma_k$ is the $k$-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the $k$-Hessian equation $\\sigma_k(D^2u)=f$ with Dirichlet boundary condition $u=0$ is variational; indeed, this problem can be studied by means of the $k$-Hessian energy $-\\int u\\sigma_k(D^2u)$. We construct a natural boundary functional which, when added to the $k$-Hessian energy, yields as its critical points solutions of $k$-Hessian equations with general non-vanishing boundary data. As a consequence, we prove a sharp Sobolev trace inequality for $k$-admissibl"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1606.00071","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-31T23:09:25Z","cross_cats_sorted":[],"title_canon_sha256":"84e47038af17130620cc1b2654690f48f94e03c92457c301a9155f22773cc79e","abstract_canon_sha256":"06a2f9855b93853a4f09817329ae67b13e7a681f2caa5a3835e9e41667e35851"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:05.971269Z","signature_b64":"9KAe1s4OKDJqfn7cEdzTj5OfTGD6wvYOwzEzXVuLGsAGvvHsqFM7Of+eWwaCkJQz39zACUNOQZCTMpEwoUIvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69b22ba747e33d9f716bb7e39117af3a023ec77791f4d967f9132e61b49cd0a9","last_reissued_at":"2026-05-18T01:13:05.970881Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:05.970881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A fully nonlinear Sobolev trace inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jeffrey S. Case, Yi Wang","submitted_at":"2016-05-31T23:09:25Z","abstract_excerpt":"The $k$-Hessian operator $\\sigma_k$ is the $k$-th elementary symmetric function of the eigenvalues of the Hessian. It is known that the $k$-Hessian equation $\\sigma_k(D^2u)=f$ with Dirichlet boundary condition $u=0$ is variational; indeed, this problem can be studied by means of the $k$-Hessian energy $-\\int u\\sigma_k(D^2u)$. We construct a natural boundary functional which, when added to the $k$-Hessian energy, yields as its critical points solutions of $k$-Hessian equations with general non-vanishing boundary data. As a consequence, we prove a sharp Sobolev trace inequality for $k$-admissibl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.00071","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1606.00071","created_at":"2026-05-18T01:13:05.970943+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.00071v1","created_at":"2026-05-18T01:13:05.970943+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.00071","created_at":"2026-05-18T01:13:05.970943+00:00"},{"alias_kind":"pith_short_12","alias_value":"NGZCXJ2H4M6Z","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NGZCXJ2H4M6Z64LL","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NGZCXJ2H","created_at":"2026-05-18T12:30:32.724797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI","json":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI.json","graph_json":"https://pith.science/api/pith-number/NGZCXJ2H4M6Z64LLW7RZCF5PHI/graph.json","events_json":"https://pith.science/api/pith-number/NGZCXJ2H4M6Z64LLW7RZCF5PHI/events.json","paper":"https://pith.science/paper/NGZCXJ2H"},"agent_actions":{"view_html":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI","download_json":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI.json","view_paper":"https://pith.science/paper/NGZCXJ2H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.00071&json=true","fetch_graph":"https://pith.science/api/pith-number/NGZCXJ2H4M6Z64LLW7RZCF5PHI/graph.json","fetch_events":"https://pith.science/api/pith-number/NGZCXJ2H4M6Z64LLW7RZCF5PHI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI/action/storage_attestation","attest_author":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI/action/author_attestation","sign_citation":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI/action/citation_signature","submit_replication":"https://pith.science/pith/NGZCXJ2H4M6Z64LLW7RZCF5PHI/action/replication_record"}},"created_at":"2026-05-18T01:13:05.970943+00:00","updated_at":"2026-05-18T01:13:05.970943+00:00"}